And that’s a great question! It seems a little absurd, doesn’t it? Equals Versus Equivalency Just because two things are equal doesn’t mean they’re equivalent. Equal is defined as, “being the same in quantity, size, degree, or value.” In the above problem 5 x 3 is equal to 5 + 5 + 5, but they’re not necessarily equivalent. I did something today I’ve never done before, I looked up the definition of multiplication. In the first definition of multiplication I found, the first factor is the number of copies and the second is the number being repeated. So if this is the definition the teacher taught, 5 x 3 is equivalent to 5 copies of 3, or 3 + 3 + 3 + 3 + 3. For example, 3 bundles of 5 bananas is different from 5 bundles of 3 bananas although they total to the same number of bananas. Here’s another example: 30 ÷ 2 is equal to 15. It depends. Why?

Games

Online Manipulatives. Professional Development By Teachers, For Teachers. Number Talks/Strings. A community for number string design. Responding to Student Progress. One area where I need a lot of growth is responding to the progress of my students.

Specifically, what are the next steps after I’ve identified the level of understanding in certain concepts? I recently decided to tackle this challenge during our review days for the state assessment. The goal was to review the most tested concepts, but I also wanted the kids to work on their biggest struggle areas. I began the process by consolidating all of the data from concept quizzes throughout the year. From there, I created a “Personal Growth Report” for each student using autoCrat. Here’s a tutorial video showing the process of creating these reports. This is a similar idea to the Growth Mindset Reports I blogged about a few months ago. For the original reports, I had the students self-assess their understanding of each concept because I was concerned about classroom status issues.

Here’s a sample… …and a link to all of the silent solutions I’ve uploaded to YouTube so far. Level 1: Level 2:
Search. Coin Box Pre-K-2, 3-5 Learn how to count, collect, exchange, and make change for coins by manipulating coins using an array representation.

Deep Sea Duel This strategy game requires you to select cards with a specified sum before your opponent (also available on iOS and Android). Dynamic Paper Pre-K-2, 3-5, 6-8, 9-12 Need a pentagonal pyramid that's six inches tall? Equivalent Fractions This applet allows you to create equivalent fractions by dividing and shading squares or circles, and match each fraction to its location on the number line. Factorize Dividing Numbers into Two Factors and Building Arrays to Represent Each Factorization.

Strict_Kakooma - GregTangMath.com. About Kakooma starts with a deceptively simple idea: in a group of numbers, find the number that is the sum of two others.

Sounds easy, right? Sometimes it is, but other times the answer is right in front of you and you just can’t see it. To solve a single puzzle, you often end up doing dozens of calculations in your head, sometimes more than a hundred! Before you know it, your mind is sharper and your math skills are better. Playing KAKOOMA Kakooma is great for people of all ages.

Multiplication

Matific. Matific. Illustrative Mathematics. The students in Ms.

Baca’s art class were mixing yellow and blue paint. She told them that two mixtures will be the same shade of green if the blue and yellow paint are in the same ratio. The table below shows the different mixtures of paint that the students made. How many different shades of paint did the students make? Some of the shades of paint were bluer than others. Draw a line connecting each point to (0,0).
ISBE Model Math Curriculum. Conferences, Webinars, Meetings.